Ellipse Construction

To start the construction, I thought about how the top half of an ellipse was symmetric to the bottom half of an ellipse. Then, I created two overlapping circles, and found the intersection points of these circles (F and G). The centers of each circle were the foci of the ellipse and realized that F and G were two points on an ellipse. I tried to move the intersection points around to trace the ellipse, but it didn't work. Moving the foci around didn't allow me to trace the ellipse either. Then, I thought about the idea that the total distance of DF and FE needs to be constant. (Similarly, the total distance of DG and GE needs to be constant as well.) Therefore, I created a line segment and used point C as my slider. The line segment AB represents the fixed distance, and I created the two circles such that the first circle had a radius equal to AC and so the second circle had a radius equal to CB using the circle with a center through point and used the compass tool to copy the circle. Then, I used the locus tool to create the ellipse. I noticed that when I used point C as a slider, I was able to reach all of the points of the ellipse.